The Smooth Approximation Algorithm For Solving The Smallest Enclosing Ball Problem

In this thesis,we mainly study the smallest enclosing ball problem which is defined as the ball with a minimum radius that encloses all the given balls in R~n.This problem arises in many applications such as location analysis,computational geometry,collision detec-tion,pattern recognition,computer graphics,artificial intelligence and military operations.Firstly,we introduce the research background of the smallest enclosing ball problem.Sec-ondly,the smallest enclosing ball problem is solved as a smooth unconstrained optimization problem by using the smooth function,and the properties of the objective function are proved.Furthermore,a smooth approximation algorithm for solving the smallest enclosing ball prob-lem is proposed,and the convergence of the algorithm is proved.Finally,numerical experiment results are given and it shows that the algorithm in this thesis is more efficient than the algorithm given in[21].